The projection of the velocity of a material point changes according to the law vx = 10 + 2t. determine

The projection of the velocity of a material point changes according to the law vx = 10 + 2t. determine the projection of the initial speed and acceleration projkts .. determine the nature of the moving point .. write the equation for the coordinates of the moving point of the material point, and the remix made by it for 10 s.

Given:

v (t) = 10 + 2 * t – the equation of the change in the speed of a material point;

t = 10 seconds.

It is required to determine the initial velocity v0, acceleration a, determine the nature of the motion, the equation of motion of the point S (t), as well as the path L traversed in time t.

We find the initial velocity at t = 0:

v0 = 10 + 2 * 0 = 10 m / s.

We find the acceleration by the derivative of the velocity equation:

a = v (t) ‘= (10 + 2 * t)’ = 2 m / s ^ 2.

Based on the initial speed and acceleration, we find that the motion of the body is uniformly accelerated, directed in the direction of increasing the X axis.

Knowing the initial speed and acceleration, we will compose the equation of motion:

S (t) = v0 * t + a * t ^ 2/2 = 10 * t + 2 * t ^ 2/2 = 10 * t + t ^ 2.

Then the distance traveled in time t will be equal to:

L = 10 * t + t ^ 2 = 10 * 10 + 10 ^ 2 = 100 + 100 = 200 meters.

Answer: the movement of the body is uniformly accelerated, with an initial speed of 10 m / s, with an acceleration of 2 m / s ^ 2, the equation of motion of the body is S (t) = 10 * t + t ^ 2, in 10 seconds the body will cover a path equal to 200 meters.